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Enter the correct answer in the box. Write your answer in the form [tex]$a t + b m \leq c$[/tex].

Denise needs to move some bags of gardening soil from her garage to her mother's garden. The topsoil weighs 30 pounds per bag, and the mulch weighs 30 pounds per bag. The wagon she is using carries a maximum of 330 pounds.

The table shows the first three loads of topsoil and mulch she has carried in the wagon.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
\begin{tabular}{c}
Topsoil, $t$ \\
(bags)
\end{tabular} & 7 & 2 & 3 \\
\hline
\begin{tabular}{c}
Mulch, $m$ \\
(bags)
\end{tabular} & 3 & 6 & 8 \\
\hline
\end{tabular}
\][/tex]

Write a linear inequality to describe the bags of topsoil and mulch the wagon can carry at one time.



Answer :

GinnyAnswer
To determine the linear inequality that describes the total weight of topsoil and mulch the wagon can carry, let's consider the following information:

1. The weight of each bag of topsoil is 30 pounds.
2. The weight of each bag of mulch is also 30 pounds.
3. The wagon can carry a maximum of 330 pounds.

Let [tex]\( t \)[/tex] represent the number of bags of topsoil.
Let [tex]\( m \)[/tex] represent the number of bags of mulch.

The total weight of topsoil in the wagon is [tex]\( 30t \)[/tex] (since each bag of topsoil weighs 30 pounds).
Similarly, the total weight of mulch in the wagon is [tex]\( 30m \)[/tex] (since each bag of mulch weighs 30 pounds).

The combined weight of both topsoil and mulch in the wagon should not exceed the maximum capacity of the wagon, which is 330 pounds.

Therefore, the linear inequality that describes the total weight of the bags of topsoil and mulch that the wagon can carry at one time is:
[tex]\[ 30t + 30m \leq 330. \][/tex]

This inequality ensures that the sum of the weights of the topsoil and mulch bags does not exceed the maximum carrying capacity of the wagon.

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